OFFSET
0,4
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..80
FORMULA
E.g.f.: Double integral of A''(x)*B(x) dx^2 where A(x) is e.g.f. for A001187 and B(x) is e.g.f. for A006125. - Geoffrey Critzer, Apr 09 2013
MAPLE
b:= proc(n) b(n):= `if`(n=0, 1, 2^binomial(n, 2)-
add(binomial(n, k)*k*b(k)*2^binomial(n-k, 2), k=0..n-1)/n)
end:
a:= n-> add(binomial(n-2, k)*b(k+2)*2^binomial(n-k-2, 2), k=0..n-2):
seq(a(n), n=0..20); # Alois P. Heinz, Apr 09 2013
MATHEMATICA
(* by brute force counting *) nn=10; g=Sum[2^Binomial[n, 2]x^n/n!, {n, 0, nn}]; a=Drop[Range[0, nn]!CoefficientList[Series[Log[g]+1, {x, 0, nn}], x], 1]; f[list_]:=Product[a[[i]], {i, list}]; Table[Total[Map[f, Map[Length, Select[SetPartitions[n], MemberQ[#[[1]], 2]&], {2}]]], {n, 2, nn}]
(* or *)
nn=30; g=Sum[2^Binomial[n, 2]x^n/n!, {n, 0, nn+2}]; Range[0, nn]!CoefficientList[Series[D[D[Log[g]+1, x], x] g, {x, 0, nn}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Apr 08 2013
EXTENSIONS
More terms from Alois P. Heinz, Apr 09 2013
STATUS
approved